Wyniki wyszukiwania - BazTech

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Quantile estimation of probability distributions for maximum daily precipitation and short time series of observational data for engineering design

Kuchar Leszek, Broszkiewicz-Suwaj Ewa

Environment Protection Engineering

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2022

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Vol. 48, nr 1

35--50

EN

Knowledge of the distribution quantiles of precipitation maximum amounts is required in many fields concerning engineering design or hydrological risk assessment. When the number of observation years is small, it is not possible to fit the probability distribution function to maximum values and to calculate quantiles. This paper presents a procedure for calculating the quantiles of the probability distribution of daily precipitation maximums over a year using stochastic convergence of distributions. The distribution series of random variables, defined based on the cut-off sample with the elimination of the smallest values, made it possible to determine the quantiles for times series of order α of the distribution. These values were approximated by a function from the exponential class and then extrapolated to obtain quantiles for the distribution of maxima. The resulting quantile estimates, for short time series, were corrected using the kurtosis of the data used for estimation, which leads to a very large error reduction.

2

Symbolic computing in probabilistic and stochastic analysis

Kamiński M.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 4

961--973

EN

The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

3

Stochastyczne równania przepływu ciepła

Pokorska I.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

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2005

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Z. 12 (160)

139-141

4

Stochastic methods in heat and mass transfer problems

Pokorska I.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

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2005

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Z. 12 (160)

133-137

5

Stochastyczne metody optymalizacji w inżynierii chemicznej i procesowej. II. Przykłady zastosowania

Jeżowski J. M., Bochenek R., Jeżowska A., Poplewski G., Słoma R.

Inżynieria i Aparatura Chemiczna

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2005

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Nr 3

3-8

PL

Artykuł jest kontynuacją pracy [1]. Przedstawiono w nim problemy optymalizacyjne z zakresu inżynierii chemicznej i procesowej rozwiązane przy użyciu metod stochastycznych opisanych w [1]. Były to nieliniowe problemy zawierające tylko zmienne ciągłe lub też zarówno zmienne dyskretne i ciągłe. We wszystkich przypadkach uzyskano wyniki uważane w literaturze za rozwiązanie globalnie optymalne.

EN

The paper presented is a continuation of the work [1]. In this part, optimization problems typical for chemical and process engineering, solved by stochastic methods described in [1] are presented. The nonlinear problems comprising only continuous or both discrete and continuous variables have been treated. In all cases, the results obtained are considered in professional literature as globally optimum solutions.

6

Zastosowanie metod stochastycznych w modelowaniu potoków ruchu na skrzyżowaniach z sygnalizacją świetlną

Sierpiński G.

Zeszyty Naukowe. Transport / Politechnika Śląska

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2003

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z. 48

301-307

PL

W artykule omówiono rozkłady opisujące strumień zgłoszeń pojazdów na skrzyżowaniu z sygnalizacją świetlną. Dokonano równocześnie weryfikacji generatora liczb pseudolosowych, losującego odstępy między zgłoszeniami pojazdów.

EN

The article deals with distribution of the flow of vehicles on the intersection with traffic lights. The generator of pseudo-random numbers drawing the time distances between vehicles has been also verified.

7

Rozszerzona metoda optymalizacji według strategii adaptacyjnego przeszukiwania losowego

Jeżowski J., Bochenek R., Słoma R., Jeżowska A., Poplewski G.

Inżynieria Chemiczna i Procesowa

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2001

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T. 22, z. 3C

567--572

PL

Praca dotyczy optymalizacji matematycznej przy zastosowaniu metody stochastycznej znanej pod nazwą adaptacyjnego przeszukiwania losowego (APL). Opisano w niej rozszerzenia i modyfikacje algorytmu Luusa-Jaakoli (LJ) z artykułu [1]. Wyniki obliczeń testowych świadczą, że zaproponowane modyfikacje zwiększają znacznie niezawodność obliczania optimum globalnego.

EN

The work deals with mathematical optimisation with the use of stochastic method commonly referred to as adaptive random search (ARS). Extensions and modifications of the algorithm presented first in [1] by Luus and Jaakola have been developed. Results of tests proved that these modifications increase largely reliability of obtaining global optimum.

8

2-D and 3-D analysis of stochastic, elastic soil medium

Przewłócki J., Górski J.

Engineering Transactions

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1999

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Vol. 47, iss. 2

173-181

EN

The paper presents a stochastic description of a three-dimensional soil medium and its modelling under strain conditions. The main aim of the paper of the paper is to work out a computational model enabling incorporation of three-dimensional variability of soil properties into the plane strain state analysis. It is assumed that the soil medium is statitically homogeneous and its mechanical behaviours is governed by the linear elasticity theory. It is also assumed that elastic parameters can be modelled as the multidimensional random fields. The strip foundation on a soil layer in the 3-D and the 2-D strain states is analysed. Stochastic 2-D and 3-D finite element methods, based on the Monte Carlo technique, were used. The analysis performed enables determination of the standard deviatios of components of the stress tensor and the displacement vector for the 3-D state, based on the solution for the 2-D plane strain state. Transfer functions between both states are determined.